Non-Relativistic Fermions Coupled to Transverse Gauge-Fields: The Single-Particle Green's Function in Arbitrary Dimension

TL;DR

This paper uses bosonization to analyze the single-particle Green's function of non-relativistic fermions coupled to transverse gauge fields across various dimensions, revealing dimension-dependent Fermi liquid behavior and Luttinger liquid characteristics.

Contribution

It provides a comprehensive calculation of the Green's function in arbitrary dimensions, showing how gauge fields affect fermionic properties and phase behavior.

Findings

Fermi liquid persists in dimensions greater than 3

Quasi-particle residue vanishes as dimension approaches 3

System exhibits Luttinger liquid behavior at d=3 and exponential decay below 3

Abstract

We use a bosonization approach to calculate the single-particle Green's function $G ( {\bf{r}} , \tau )$ of non-relativistic fermions coupled to transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$ transverse gauge-fields do not destroy the Fermi liquid, although for $d < 6$ the quasi-particle damping is anomalously large. For $d \rightarrow 3$ the quasi-particle residue vanishes as $Z \propto \exp [ - \frac{1}{2 \pi ( d-3)} (\frac{ \kappa}{mc } )^2 ]$, where $\kappa$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and $c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger liquid, with anomalous dimension $\gamma_{\bot} = \frac{1}{6 \pi} ( \frac{ \kappa}{mc} )^2$. For $d < 3$ we find that $G ({\bf{r}} , 0 )$ decays exponentially at large distances.